In my geometry textbook it is stated that intuitively we can choose a suitable basis of coordinates that the components Christoffel symbol vanishes locally at that point(= 0). However can one obtain a formal proof of it? For example if we use rectification theorem to rectify the geodesics passing through a point into straight lines, can we say under such diffeomorphism the Christoffel symbol vanishes since the geodesic is mapped into a line in the neighbourhood of that point?(adsbygoogle = window.adsbygoogle || []).push({});

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# Question about Christoffel symbol's value

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